Random dynamical systems for stochastic partial differential equations driven by a fractional Brownian motion

Abstract

In this paper we study nonlinear stochastic partial differential equations (SPDEs) driven by a fractional Brownian motion (fBm) with the Hurst parameter bigger than 1/2. We show that these SPDEs generate random dynamical systems (or stochastic flows) by using the stochastic calculus for an fBm where the stochastic integrals are defined by integrands given by fractional derivatives. In particular, we emphasize that the coefficients in front of the fractional noise are non-trivial.